HIV-related illness is and will continue to be an important clinical and public health issue as well an international security, stability, and development issue. Although the advent of Highly Active Anti-Retroviral Therapy (HAART) has significantly reduced HIV-related morbidity and mortality, further advances in the treatment of HIV-infected individuals require a deeper understanding of the underlying mechanisms of the disease and how they are affected by these powerful treatments. For example, whether individuals may interrupt or discontinue treatment with control of infection is an important clinical question, insight into which may be gained by improved understanding of disease mechanisms. Indeed, as not all individuals experience the same level of treatment efficacy, it is imperative that variation in these mechanisms across individuals be elucidated. Mathematical models, in the form of systems of ordinary and delay differential equations, have been used to provide descriptions of the dynamics of the interactions of HIV and various compartments of the human immune system and thus formalize theorized mechanisms and have led to considerable recent insights. However, only simplified such models have been tested with clinical data; thus, there remain significant opportunities for mathematical modeling to contribute to enhanced understanding of HIV infection and associated immune response. The investigators will use advanced mathematical modeling and relevant statistical methods to develop new models for interactions among HIV, its target resources (T-cells, macrophages and/or dendritic cells), and the human immune system, with a particular emphasis on building models on the basis of clinical data wherever possible. They will test for and analyze nonlinear mathematical mechanisms in HIV infection dynamics and associated immune response using both ordinary and partial differential equations. In situations where data analysis suggests that nonlinearities in the models that describe the biology are relevant, they will perform numerical and/or qualitative analysis of the systems to identify stable behavior and bifurcations in the mathematical system, which in turn could provide insight into control of the biological system. Furthermore, they will develop and implement formal statistical and computational methods to estimate parameters in the models with emphasis on accounting for and exploring variability underlying mechanisms across different individuals. Finally. they will use the models and methods to address specific scientific questions, including analysis of differences in dynamic parameters based on a variety of host genotypes and development of optimal control methodologies designed to guide for structured treatment interruptions of HIV therapy.